Squares in partial words
نویسندگان
چکیده
منابع مشابه
Squares in Binary Partial Words
In this paper, we investigate the number of positions that do not start a square, the number of square occurrences, and the number of distinct squares in binary partial words. Letting σh(n) be the maximum number of positions not starting a square for binary partial words with h holes of length n, we show that limσh(n)/n = 15/31 provided the limit of h/n is zero. Letting γh(n) be the minimum num...
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A well known result of Fraenkel and Simpson states that the number of distinct squares in a word of length n is bounded by 2n since at each position there are at most two distinct squares whose last occurrence start. In this paper, we investigate the problem of counting distinct squares in partial words, or sequences over a finite alphabet that may have some “do not know” symbols or “holes” (a ...
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Well-known results on the avoidance of large squares in (full) words include the following: (1) Fraenkel and Simpson showed that we can construct an infinite binary word containing at most three distinct squares; (2) Entringer, Jackson and Schatz showed that there exists an infinite binary word avoiding all squares of the form xx such that |x| ≥ 3, and that the bound 3 is optimal; (3) Dekking s...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2014
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2014.02.023